Solving Compound Inequality with "And" and "Or": To solve any compound inequality, we follow some steps:(1) First solve each inequality separately.

(2) Add or subtract the number term on each side of both terms.

(3) Multiply or divide of each side of both inequalities, by the required number. If we multiply any inequality by a number with the negative sign then sign of inequality will change.

(4) We just remember the thing that the word "and" indicates the overlap or intersection is the required result and the word "or" indicates combine the solutions i.e. find the union of the solution sets of each inequality.

Here x < 3 indicates all the numbers to he left sides of 3 and x > -6 indicates all the numbers to the right sides of -6.So the intersection of these two is all the number between -6 and 3. The solution set is { x I x >-6 and x < 3 }.Graph of above:

Example 2: Solve for x: 3x + 6 < -12 or -4x + 1 < 13Solution: First solve each inequality separately, the word "or" indicates combine the answers i.e. find the union of the solution sets of each inequality. 3x + 6 < -12 or -4x + 1 < 13Subtract 6 both sides in first inequality and subtract 1 both sides in the second inequality,

3x + 6 -6 < -12 -6 or -4x + 1 -1 < 13 -1

$\Rightarrow$ 3x < -18 or -4x < 12

Divided first inequality by 3 and second by -4( when we divided second inequality by -4, then the sign of inequality is changed).